Answer
$\frac{16\sqrt{6a}}{6a}$
Work Step by Step
$\frac{16a}{\sqrt{6a^3}}\longrightarrow$ factor perfect square out of $6a^3$
=$\frac{16a}{\sqrt{a^2\times6a}}\longrightarrow$ multiplication property of square roots
=$\frac{16a}{\sqrt{a^2}\times\sqrt{6a}}\longrightarrow$ simplify
=$\frac{16/\!\!a}{/\!\!a\sqrt{6a}}\longrightarrow$ multiply numerator and denominator by $\sqrt{6a}$; a cancels in numerator and denominator
=$\frac{16}{\sqrt{6a}}\times\frac{\sqrt{6a}}{\sqrt{6a}}\longrightarrow$ simplify
=$\frac{16\sqrt{6a}}{6a}$
